Optical tomography optoelectronic arrangements for microplate wells

ABSTRACT

Optical tomography arrangements are disclosed for performing optical tomography on the transparent or translucent contents of individual microplate wells comprising a light emitting array having a plurality of light emitting elements, a sample module, and a light sensing array including a plurality of light sensing elements, wherein the light sensing array is configured to sense light emitted from the light emitting array which has passed through the sample module. The light emitting elements can comprise light emitting diodes (LEDs), organic light emitting diodes (OLEDs), organic light emitting transistors (OLETs), and/or other optoelectronic devices. The light sensing array can comprise organic light sensing devices, photodiodes, phototransistors, CMOS photodetectors, or charge-coupled devices (CCDs). The light emitting array can be flat or curved, and the light sensing array can be flat or curved. The collection of measurement values can be overspecified, and a generalized inverse operation can provide solutions rendering computational tomography data.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is a continuation application of U.S. application Ser.No. 15/457,963, entitled “CYLINDRICAL OPTICAL TOMOGRAPHY FOR MICROSCOPY,CELL CYTOMETRY, MICROPLATE ARRAY INSTRUMENTATION, CRYSTALLOGRAPHY, ANDOTHER APPLICATIONS,” filed Mar. 13, 2017 which is a Continuation of U.S.application Ser. No. 13/963,931, entitled “OPTICAL TOMOGRAPHY FORMICROSCOPY, CELL CYTOMETRY, MICROPLATE ARRAY INSTRUMENTATION,CRYSTALLOGRAPHY, AND OTHER APPLICATIONS,” filed Aug. 9, 2013, (U.S. Pat.No. 9,594,019, issued Mar. 14, 2017) the disclosure of which isincorporated herein in its entirety by reference.

COPYRIGHT & TRADEMARK NOTICES

A portion of the disclosure of this patent document may containmaterial, which is subject to copyright protection. Certain marksreferenced herein may be common law or registered trademarks of theapplicant, the assignee or third parties affiliated or unaffiliated withthe applicant or the assignee. Use of these marks is for providing anenabling disclosure by way of example and shall not be construed toexclusively limit the scope of the disclosed subject matter to materialassociated with such marks.

BACKGROUND OF THE INVENTION Field of the Invention

The present invention pertains to tomography and 3D imaging, and morespecifically to optical tomography for microscopy, cell cytometry,microplate array instrumentation, and other applications.

Overview of the Invention

Tomography refers to computational imaging by sections or sectioning viathe use of any kind of penetrating wave, such as x-rays, gamma rays,radio-frequency waves, light, etc. has can be produced byelectron-positron annihilation, electrons, ions, magnetic particles,light source, etc. Optical tomography is a form of computed tomographythat creates a digital volumetric model of an object by reconstructingimages made from light transmitted and scattered through an object.Optical tomography relies on the object under study being at leastpartially optically transparent. The present invention presentsapplications and opportunities in optical tomography which have remainedlargely unexplored and undeveloped. Light emitting diodes, or LEDs, haveboth light emitting and sensing properties. With the abundance of highand low performance LEDs at an economical price, leveraging theproperties of LEDS, organic LEDs (OLEDs), etc., provides an importantreason to consider such an invention. For example, OLEDs arrays arealready in wide use in many types of electronic displays and they can befabricated via printed electronics on a variety of surfaces such asglass, mylar, plastics, paper, etc. Leveraging some of the properties ofsuch materials, LED arrays can be readily bent, printed on curvedsurfaces, etc. Such properties create vast opportunities for 3-D imagingin areas such as microscopy, cell cytometry, microplate arrayinstrumentation, and other applications.

BRIEF DESCRIPTION OF THE DRAWINGS

The above and other aspects, features and advantages of the presentinvention will become more apparent upon consideration of the followingdescription of preferred embodiments taken in conjunction with theaccompanying drawing figures, wherein:

FIG. 1 shows an example embodiment of a planar light emitting and lightsensing arrangement in an optical tomography system.

FIG. 2 depicts an optimization space for semiconductor diodes comprisingattributes of signal switching performance, light emitting performance,and light detection performance.

FIG. 3 depicts an example metric space representation of devicerealizations for optoelectronic devices and regions of optimization andco-optimization.

FIG. 4a shows an example schematic diagram of a light-emitting LEDarrangement.

FIG. 4b shows an example schematic diagram of a light-sensing LED in areverse-bias arrangement.

FIG. 4c shows an example schematic diagram of a light-sensing LEDarrangement for measuring decay time.

FIG. 5 depicts an example multiplexing arrangement for a two-dimensionalarray of LEDs.

FIG. 6 depicts an adaptation of the arrangement depicted in FIG. 5 thatis controlled by an address decoder so that the selected subset can beassociated with a unique binary address.

FIG. 7 depicts an example adaptation of the arrangement of FIG. 6together to form a highly scalable LED array display that also functionsas a light field detector.

FIGS. 8 and 9 depict example functional cells that can be used in alarge scale array.

FIGS. 10-13 depict various example circuits demonstrating variousexample approaches to detecting light with an LED.

FIGS. 14-16 depict adaptations of the digital circuit measurement anddisplay arrangements into an example combination.

FIGS. 17-20 depict example state diagrams for the operation of the LEDand the use of input signals and output signals.

FIGS. 21a-21d shows example geometries of light emitting and lightsensing arrangements for various optical tomography systems.

FIG. 22 shows an example embodiment of a discretized space between aplanar light emitting and light sensing arrangement in an opticaltomography system.

FIG. 23a shows an example of three-dimensional space between a planarlight emitting and light sensing arrangement.

FIG. 23b shows an example of a discretized three-dimensional spacebetween a planar light emitting and light sensing arrangement.

FIG. 24a depicts an example light path between a light emission planeand a light sensing plane in three-dimensional space.

FIG. 24b depicts an example activation of discrete voxels intersected bythe light path in discretized three-dimensional space.

FIG. 24c further depicts an example activation of discrete voxelsintersected by the light path in discretized three-dimensional space.

FIG. 25a depicts discretized planes in a discretized space, shown withvoxels activated by multiple light paths.

FIG. 25b depicts an example cross-sectional view of a voxel arrangementin a discretized space.

FIG. 26a depicts an example cascade of identical light transmission losslayers illustrating Beer's law.

FIG. 26b depicts an example set of data based on FIG. 26a showing arelationship between path length of light and light transmittance.

FIG. 27a depicts an example cascade of non-uniform light losstransmission through objects of different thicknesses.

FIG. 27b depicts an example set of data based on FIG. 27a showing arelationship between transmittance and percentage of light loss.

FIG. 28a depicts example aperture effects between a light emitting andlight sensing arrangement in an optical tomography system.

FIG. 28b depicts an example graph showing the relationship betweenmagnitude of light sensed by a light sensing arrangement and theincident angle of the light path.

FIG. 29 depicts an example empirical aperture measurement andnormalization flow chart to account for aperture effects that may occurbetween light emitting and light sensing arrangement in discretizedthree-dimensional space.

FIG. 30a depicts an example planar geometry light emitting and lightsensing arrangement wherein the emitting and sensing planes are of thesame dimensions.

FIG. 30b depicts an example planar geometry light emitting and lightsensing arrangement wherein the emitting and sensing planes are ofdifferent dimensions.

FIG. 31 depicts an example planar geometry light emitting and sensingarrangement wherein the distance between emitting and sensing planes isreduced.

FIG. 32 depicts an example measurement data scanning and acquisitionflow chart for data gathered by the light sensing array about an objectplaced between light emitting and light sensing arrangement indiscretized three-dimensional space.

FIG. 33 depicts an example measurement data processing flow chart fordata gathered by the light sensing array about an object placed betweenlight emitting and light sensing arrangement in discretizedthree-dimensional space.

FIG. 34 depicts an example hardware and software architectureimplementation in an optical tomography system for a data path.

FIG. 35 depicts an example method illustrating steps in the flow of thedata path of the invention.

FIG. 36a depicts an example of refraction of a light path transmittedthrough a transparent object between light emitting and light sensingarrangement.

FIG. 36b depicts an example of light scattering of a light pathtransmitted through a translucent object between light emitting andlight sensing arrangement.

FIG. 36c depicts an example of reflection of a light path through atransparent object between light emitting and light sensing arrangement.

FIG. 37a depicts an example light emitting and light sensing arrangementwith cylindrical geometry in an optical tomography system.

FIG. 37b depicts the arrangement of FIG. 37a with a row-like arrangementof LEDs in a cylindrically shaped system.

FIG. 37c depicts the LED arrangement of FIG. 37b with an arrangement ofLEDs on a front side and back side of the cylindrically shaped system.

FIG. 37d depicts an example side view of emitting LED from the back sideof the cylindrically shaped system to the front side.

FIG. 37e depicts an example emitting LED emitting light in and amongLEDs in an emitting array from the back side of the cylindrically shapedsystem to the front side wherein a plurality of sensing LEDs sense theemitted light among LEDs in a sensing array.

FIG. 37f depicts an example emitting LED emitting light from the backside of the cylindrically shaped system to the front side wherein aplurality of sensing LEDs sense the emitted light.

FIG. 37g depicts a more detailed and rotated view of the cylindricalarrangement of FIG. 37a , showing an emitting array and a sensing array.

FIG. 37h depicts a top view of an example discretization of a lightemitting and light sensing arrangement with cylindrical geometry in anoptical tomography system.

FIG. 38 shows an example embodiment of a discretization of space in acylindrical light emitting and light sensing arrangement in an opticaltomography system.

FIGS. 39a-39c show multiple views of an example embodiment of adiscretization of space for a cylindrical light emitting and lightsensing arrangement in an optical tomography system.

FIGS. 40a-40b show an example embodiment of a discretization of spacefor a cylindrical light emitting and light sensing arrangement in anoptical tomography system, wherein FIG. 40b shows increaseddiscretization.

FIGS. 41a-41b depict an example activation of discrete voxelsintersected by a light path in discretized three-dimensional space in acylindrical arrangement in an optical tomography system.

FIG. 42a illustrates an example sample holding module, as a slide with awell for a planar light emitting and light sensing arrangement in anoptical tomography system for cytometry.

FIG. 42b illustrates a side view of the example holding module of FIG.42 a.

FIG. 43a illustrates an example holding module, as a pathway for aplanar light emitting and light sensing arrangement in an opticaltomography system.

FIG. 43b illustrates a side view of the example holding module of FIG.43 a.

FIG. 44a illustrates an example holding module, as a belt configurationfor a planar light emitting and light sensing arrangement in an opticaltomography system.

FIG. 44b illustrates a side view of the example holding module of FIG.44 a.

FIG. 45a illustrates an example holding module, as a shell configurationfor a planar light emitting and light sensing arrangement in an opticaltomography system.

FIG. 45b illustrates another example holding module, as a shellconfiguration for a planar light emitting and light sensing arrangementin an optical tomography system.

FIG. 45c illustrates yet another example holding module, as a shellconfiguration for a planar light emitting and light sensing arrangementin an optical tomography system.

FIG. 46a illustrates an example holding module, as a handleconfiguration for a planar light emitting and light sensing arrangementin an optical tomography system.

FIG. 46b illustrates an example holding module, as a hook configurationfor a planar light emitting and light sensing arrangement in an opticaltomography system.

FIG. 46c illustrates the example holding module of FIG. 46a , whereinthe handle is placed at a different location.

FIG. 46d illustrates an example holding module, as a bell configuration.

FIG. 46e illustrates the light emitting and sensing arrays of theholding module of FIG. 46 d.

FIG. 47a shows an example graphical rendering in a visualizer module ofthree-dimensional space between a planar light emitting and lightsensing arrangement.

FIG. 47b shows an example graphical rendering in a visualizer module ofa discretized three-dimensional space between a planar light emittingand light sensing arrangement.

FIG. 48a depicts an example graphical rendering in a visualizer moduleof a light path between a light emission plane and a light sensing planein three-dimensional space.

FIG. 48b depicts an example graphical rendering in a visualizer moduleof an activation of discrete voxels intersected by the light path indiscretized three-dimensional space.

FIG. 48c further depicts an example graphical rendering in a visualizermodule of an activation of discrete voxels intersected by the light pathin discretized three-dimensional space.

FIG. 49a depicts an example graphical rendering in a visualizer moduleof discretized planes in a discretized space, shown with voxelsactivated by multiple light paths.

FIG. 49b depicts an example graphical rendering in a visualizer moduleof a cross-sectional view of a voxel arrangement in a discretized space.

FIG. 50 depicts an example embodiment of a fluorescence detectionapplication with a planar light emitting and light sensing arrangementin an optical tomography system.

FIG. 51 depicts an example embodiment of a flow cytometry applicationwith a cylindrical light emitting and light sensing arrangement in anoptical tomography system.

FIG. 52a illustrates an example embodiment of the present invention as amicroplate.

FIG. 52b illustrates a side view of FIG. 52 a.

FIG. 53 depicts an example embodiment of a microplate with a planarlight emitting and light sensing arrangement in an optical tomographysystem.

FIG. 54 depicts another example embodiment microplate with a planarlight emitting and light sensing arrangement in an optical tomographysystem.

FIG. 55a depicts an example embodiment of a microplate with a planarlight emitting and light sensing arrangement applied to each well of themicroplate in an optical tomography system.

FIG. 55b depicts an example embodiment of a microplate with acylindrical light emitting and light sensing arrangement applied to eachwell of the microplate in an optical tomography system.

FIG. 56a depicts an example embodiment of a culture dish with a planarlight emitting and light sensing arrangement in an optical tomographysystem.

FIG. 56b depicts an example embodiment of a culture dish with acylindrical light emitting and light sensing arrangement in an opticaltomography system.

FIG. 57 depicts an example embodiment of a microfluidic plate with aplanar light emitting and light sensing arrangement in an opticaltomography system.

FIG. 58 depicts another example microfluidic plate with a planar lightemitting and light sensing arrangement in an optical tomography system.

FIG. 59 depicts an example embodiment of a culture chamber, with aplanar light emitting and light sensing arrangement in an opticaltomography system.

DETAILED DESCRIPTION

In the following description, reference is made to the accompanyingdrawing figures which form a part hereof, and which show by way ofillustration specific embodiments of the invention. It is to beunderstood by those of ordinary skill in this technological field thatother embodiments may be utilized, and structural, electrical, as wellas procedural changes may be made without departing from the scope ofthe present invention.

In the following description, numerous specific details are set forth toprovide a thorough description of various embodiments. Certainembodiments may be practiced without these specific details or with somevariations in detail. In some instances, certain features are describedin less detail so as not to obscure other aspects. The level of detailassociated with each of the elements or features should not be construedto qualify the novelty or importance of one feature over the others.

1. Light Sourcing and Light Sensing

FIG. 1 shows an example embodiment of a planar light emitting and lightsensing arrangement in an optical tomography system, depicting variouselements of the system such as light emitting and light sensing arrays,each comprised of LEDs, and a holding module. FIG. 1 is illustrative inits depiction of an embodiment of the present invention but notrestrictive.

Light sourcing or emitting and light sensing arrangements of the presentinvention can be an array of light emitting (light emitter) or lightsensing (light sensor) elements. In an example embodiment, as shown inFIG. 1, a planar 2-dimensional light sensing or light sensor array and aplanar 2-dimensional light emitting or light emission array face eachother in a parallel arrangement configured so each sensor in the lightsensor plane can receive light emitted by at least one light emitter orlight emitting element in the light emitter plane. In a planararrangement, the light emitting and light sensing arrays have n by n orn² LEDs and there will be at most n⁴ light paths because each light pathis defined by a pairing of light emitting and light sensing LEDs andthere are n²×n²=n⁴ possible pairings of light emitting to light sensingLEDs. The quantity and arrangement of light emitting and light sensingelements can vary depending on the geometric arrangement.

1.1 Light Sourcing and Light Sensing Technologies

Light emitting and light sensing elements can comprise light-emittingdiodes (LEDs), thin-film/printed organic light-emitting diodes (OLEDs),thin-film/printed organic light-emitting transistors (OLETs), etc. Invarious implementations the resolutions and spatial layout of the arrayof light-emitting elements can match, exceed, or be less than that ofthe image sensor pixel array as can be advantageous for reasons offunction, cost, performance, etc. Further, the high-density array oflight-emitting elements can comprise light-emitting elements of variouswavelengths as can be advantageous in producing traditional opticalcolor images and/or special scientific images, i.e., ultraviolet LEDs.It is also noted that LEDs behave as (wavelength sensitive) photodiodes.Thus, an LED array can be used as an image sensing array. Additionally,individual elements in an LED array can be switched between inactive (oridle) mode, light-emitting mode, and light-sensing mode.

Such an arrangement, if used as an image sensor, can be sequentiallyoperated to produce reflected-light contact imaging. In animplementation, the illuminating LED array is used both as asequentially scanned light source and, via sequencing and/ormultiplexing, as a reflective-imaging light sensor. High resolutionsensors or organic light sensors that are not LEDs especially in planargeometry arrangement can also be implemented in certain embodiments ofthe present invention. In some embodiments, LEDs with both emitting andsensing properties require co-optimizing of both sets of properties. Inother embodiments, LEDs with strictly emitting properties or LEDs withstrictly detecting properties might be advantageous to optimizeperformance. For example, as illustrated in pending U.S. patentapplication Ser. No. 13/180,345, FIG. 2 depicts an optimization spacefor semiconductor diodes comprising attributes of signal switchingperformance, light emitting performance, and light detectionperformance. Specific diode materials, diode structure, and diodefabrication approaches can be adjusted to optimize a resultant diode forswitching function performance (for example, via use of abruptjunctions), light detection performance such as via a P-I-N structurecomprising a layer of intrinsic semiconducting material between regionsof n-type and p-type material, or light detection performance. FIG. 3depicts an example metric space representation of device realizationsfor optoelectronic devices and regions of optimization andco-optimization. Specific optoelectrical diode materials, structure, andfabrication approaches can be adjusted to optimize a resultantoptoelectrical diode for light detection performance such as via a P-I-Nstructure comprising a layer of intrinsic semiconducting materialbetween regions of n-type and p-type material versus light emissionperformance versus cost Optimization within the plane defined by lightdetection performance and cost traditionally result in photodiodes whileoptimization within the plane defined by light emission performance andcost traditionally result in LEDs. Specific optoelectrical diodematerials, structure, and fabrication approaches can be adjusted toco-optimize an optoelectrical diode for both good light detectionperformance and light emission performance versus cost. A resultingco-optimized optoelectrical diode can be used for multiplexed lightemission and light detection modes. These permit a number ofapplications of the present invention.

FIG. 4a shows an example schematic diagram of a light-emitting LEDarrangement. In contrast to FIG. 4a , FIG. 4b shows an example schematicdiagram of a light-sensing LED in a reverse-bias arrangement. FIG. 4cshows an example schematic diagram of a light-sensing LED arrangementfor measuring decay time. Pending U.S. patent application Ser. No.13/180,345 explains how light sensing is typically performed byphotosite CCD (charge-coupled device) elements, phototransistors,complementary metal-oxide-semiconductor (CMOS) photodetectors, andphotodiodes. Photodiodes are often viewed as the simplest and mostprimitive of these, and typically comprise a PIN(P-type/Intrinsic/N-type) junction rather than the more abrupt PIN(P-type/N-type) junction of conventional signal and rectifying diodes.However, virtually all diodes are capable of photoelectric properties tosome extent. In particular, LEDs, which are diodes that have beenstructured and doped specific types of optimized light emission, canalso behave as (at least low-to moderate performance) photodiodes. EachLED in an array of LEDs can be alternately used as a photodetector or asa light emitter. At any one time, each individual LED would be in one ofthree states, a light emission mode, a light detection mode, or aninactive (or idle) mode as can be advantageous for various operatingstrategies. The state transitions of each LED can be coordinated in awide variety of ways to afford various multiplexing, signaldistribution, and signal gathering schemes as can be advantageous.

1.2 Multiplexing

A variety of methods can be implemented for the multiplexing circuitryfor LED arrays utilized in the present invention. As illustrated inpending U.S. patent application Ser. No. 13/180,345, for rectangulararrays of LEDs, it is typically useful to interconnect each LED withaccess wiring arranged to be part of a corresponding matrix wiringarrangement. The matrix wiring arrangement is time-division multiplexed.Such time-division multiplexed arrangements can be used for deliveringvoltages and currents to selectively illuminate each individual LED at aspecific intensity level (including very low or zero values so as to notilluminate).

An example multiplexing arrangement for a two-dimensional array of LEDsis depicted in FIG. 5. Here each of a plurality of normally-open analogswitches are sequentially closed for brief disjointed intervals of time.This allows the selection of a particular subset (here, a column) ofLEDs to be grounded while leaving all other LEDs in the array notconnected to ground. Each of the horizontal lines then can be used toconnect to exactly one grounded LED at a time. The plurality ofnormally-open analog switches in FIG. 5 can be controlled by an addressdecoder so that the selected subset can be associated with a uniquebinary address, as suggested in FIG. 6. The combination of the pluralityof normally-open analog switches together with the address decoder forman analog line selector. By connecting the line decoder's addressdecoder input to a counter, the columns of the LED array can besequentially scanned.

FIG. 7 depicts an example adaptation of the arrangement of FIG. 6together to form a highly scalable LED array display that also functionsas a light field detector. The various multiplexing switches in thisarrangement can be synchronized with the line selector and mode controlsignal so that each LED very briefly provides periodically updateddetection measurement and is free to emit light the rest of the time. Awide range of variations and other possible implementations are possibleand implemented in various embodiments of the present invention.

Such time-division multiplexed arrangements can alternatively be usedfor selectively measuring voltages or currents of each individual LED.Further, the illumination and measurement time-division multiplexedarrangements themselves can be time-division multiplexed, interleaved,or merged in various ways. As an illustrative example, the arrangementof FIG. 7 can be reorganized so that the LED, mode control switch,capacitor, and amplifiers are collocated, for example as in theillustrative example arrangement of FIG. 8. Such an arrangement can beimplemented with, for example, three MOSFET switching transistorconfigurations, two MOSFET amplifying transistor configurations, asmall-area/small-volume capacitor, and an LED element (that is, fivetransistors, a small capacitor, and an LED). This can be treated as acell which is interconnected to multiplexing switches and control logic.A wide range of variations and other possible implementations arepossible and the example of FIG. 7 is in no way limiting. For example,the arrangement of FIG. 7 can be reorganized to decentralize themultiplexing structures so that the LED, mode control switch,multiplexing and sample/hold switches, capacitor, and amplifiers arecollocated, for example as in the illustrative example arrangement ofFIG. 9. Such an arrangement can be implemented with, for example, threeMOSFET switching transistor configurations, two MOSFET amplifyingtransistor configurations, a small-area/small-volume capacitor, and anLED element (that is, five transistors, a small capacitor, and an LED).This can be treated as a cell whose analog signals are directlyinterconnected to busses. Other arrangements are also possible.

The discussion and development thus far are based on the analog circuitmeasurement and display arrangement of FIG. 10 that in turn leveragesthe photovoltaic properties of LEDs. With minor modifications clear toone skilled in the art, the discussion and development thus far can bemodified to operate based on the analog circuit measurement and displayarrangements of FIG. 11 and FIG. 12 that leverage the photocurrrentproperties of LEDs.

FIG. 14, FIG. 15, and FIG. 16 depict an example of how the digitalcircuit measurement and display arrangement of FIG. 13 (that in turnleverages discharge times for accumulations of photo-induced charge inthe junction capacitance of the LED) can be adapted into theconstruction developed thus far. FIG. 14 adapts FIG. 13 to additionalinclude provisions for illuminating the LED with a pulse-modulatedemission signal. Noting that the detection process described earlier inconjunction with FIG. 13 can be confined to unperceivably shortintervals of time, FIG. 15 illustrates how a pulse-width modulatedbinary signal can be generated during LED illumination intervals to varyLED emitted light brightness. FIG. 16 illustrates an adaptation of thetri-state and Schmitt-trigger/comparator logic akin to that illustratedin the microprocessor I/O pin interface that can be used to sequentiallyaccess subsets of LEDs in an LED array as described in conjunction withFIG. 5 and FIG. 6.

FIGS. 17-19 depict example state diagrams for the operation of the LEDand the use of input signals and output signals described above. Fromthe viewpoint of the binary mode control signal there are only twostates: a detection state and an emission state, as suggested in FIG.17. From the viewpoint of the role of the LED in a larger systemincorporating a multiplexed circuit arrangement such as that of FIG. 7,there can be a detection state, an emission state, and an idle state(where there is no emission nor detection occurring), obeying statetransition maps such as depicted in FIG. 18 or FIG. 19. At a furtherlevel of detail, there are additional considerations. To emit light, abinary mode control signal can be set to “emit” mode (causing the analogswitch to be closed) and the emission light signal must be of sufficientvalue to cause the LED to emit light (for example, so that the voltageacross the LED is above the “turn-on” voltage for that LED). If thebinary mode control signal is in “emit” mode but the emission lightsignal is not of such sufficient value, the LED will not illuminate.This can be useful for brightness control (via pulse-width modulation),black-screen display, and other uses. In some embodiments, this can beused to coordinate the light emission of neighboring LEDs in an arraywhile a particular LED in the array is in detection mode. If theemission light signal of such sufficient value but the binary modecontrol signal is in “detect” mode, the LED will not illuminateresponsive to the emission light signal. This allows the emission lightsignal to be varied during a time interval when there is no lightemitted, a property useful for multiplexing arrangements. During a timeinterval beginning with the change of state of the binary mode controlsignal to some settling-time period afterwards, the detection outputand/or light emission level may momentarily not be accurate. To detectlight, the binary mode control signal must be in “detect” mode (causingthe analog switch to be open). The detected light signal can be used bya subsequent system or ignored. Intervals where the circuit is indetection mode but the detection signal is ignored can be useful formultiplexing arrangement, in providing guard-intervals for settlingtime, to coordinate with the light emission of neighboring LEDs in anarray, etc.

FIG. 20 depicts an example state transition diagram reflecting the aboveconsiderations. The top “Emit Mode” box and bottom “Detect Mode” boxreflect the states of an LED from the viewpoint of the binary modecontrol signal as suggested by FIG. 17. The two “Idle” states (one ineach of the “Emit Mode” box and “Detect Mode” box) of FIG. 20 reflect(at least in part) the “Idle” state suggested in FIG. 18 and/or FIG. 19.Within the “Emit Mode” box, transitions between “Emit” and “Idle” can becontrolled by emit signal multiplexing arrangements, algorithms forcoordinating the light emission of an LED in an array while aneighboring LED in the array is in detection mode, etc. Within the“Detect Mode” box, transitions between “Detect” and “Idle” can becontrolled by independent or coordinated multiplexing arrangements,algorithms for coordinating the light emission of an LED in an arraywhile a neighboring LED in the array is in detection mode, etc. Inmaking transitions between states in the boxes, the originating andtermination states can be chosen in a manner advantageous for details ofvarious multiplexing and feature embodiments. Transitions between thegroups of states within the two boxes correspond to the vast impedanceshift invoked by the switch opening and closing as driven by the binarymode control signal. In FIG. 20, the settling times between these twogroups of states are gathered and regarded as a transitional state.

As mentioned earlier, the amplitude of light emitted by an LED can bemodulated to lesser values by means of pulse-width modulation (PWM) of abinary waveform. For example, if the binary waveform oscillates betweenfully illuminated and non-illuminated values, the LED illuminationamplitude will be perceived roughly as 50% of the full-on illuminationlevel when the duty-cycle of the pulse is 50%, roughly as 75% of thefull-on illumination level when the duty-cycle of the pulse is 75%,roughly as 10% of the full-on illumination level when the duty-cycle ofthe pulse is 10%, etc. Clearly the larger fraction of time the LED isilluminated (i.e., the larger the duty-cycle), the brighter theperceived light observed emitted from the LED.

It is further understood that depending on the embodiments of lightsourcing and sensing arrangements of the present invention, variouscombinations and modifications of multiplexing circuitry can beimplemented to achieve the desired result. It is further understood thatsuch multiplexing circuitry can further be combined and modified tobetter utilize the properties of flexible materials onto which the lightLEDs, OLEDs, etc. are printed.

1.3 Light Sourcing and Light Sensing Geometries

FIGS. 21a-21d shows example geometries of light emitting and lightsensing arrangements for various optical tomography systems. Variouslight emitting and light sensing arrangement geometries suitable foroptical tomography include, but are not limited to planar, cylindrical,spherical, or warped (i.e., flexible). For example, FIG. 21a shows anexample light emitting and light sensing arrangement with planargeometry. FIG. 21b shows an example light emitting and light sensingarrangement with cylindrical geometry. FIG. 21c shows an example lightemitting and light sensing arrangement with spherical geometry. FIG. 21dshows an example light emitting and light sensing arrangement withwarped, or flexible geometry. In certain embodiments, one plane or onehalf of the arrangement can act as a light sensing array and the otherplane or half can act as a light emitting or light emission array, orboth planes or both halves can have both light emitting and lightsensing capabilities. Depending on the physical characteristics of theobject or specimen, the medium in which the object is located, size,opacity, etc., various geometric arrangements can be advantageous andcan be implemented in different embodiments of the present invention. Itis also noted that in certain embodiments of the invention, flexible,printable materials can be used to achieve a variety of geometricarrangements of the present invention.

1.4 Discretization of 3-D Space in Measurement Volume

FIG. 22 shows an example embodiment of a discretized space between aplanar light emitting and light sensing arrangement in an opticaltomography system. In order to calculate the transparency of an objectplaced between a light emitting and light sensing arrangement with highresolution, a set of mathematical equations for processing can begenerated. To generate mathematical equations, space between the lightemitting and light sensing arrangement is discretized, such as into aplurality of cubes, or voxels, as depicted in FIG. 22, which shows anexample embodiment of a discretized space between a planar lightemitting and light sensing arrangement in an optical tomography system.These cubes act as 3D pixels, or voxels, and are interrogated togenerate a full reconstruction of the object. Just as a camera capturesa 2D image by interrogating and replicating the color of each pixel inthe image, the present invention renders a 3D model of an object byinterrogating and replicating the opacity of each voxel in the object.

FIG. 23a shows an example of three-dimensional space between a planarlight emitting and light sensing arrangement. FIG. 23b shows an exampleof a discretized three-dimensional space between a planar light emittingand light sensing arrangement. Generally, an increase in thediscretization of the space into smaller units provides a more detailedcalculation of the transparency of the object and hence, a higherresolution. The set of equations and associated computations will varyin complexity based on the geometry of the arrangement.

In an example embodiment, the space between the light emitting and lightsensing arrangement is divided into voxels as in FIG. 23b . One LED onthe light emitting array would transmit every possible light path (as acone of light) through the discretized space between the emitting LEDand each light sensing element on the light sensing array. For example,FIG. 24a depicts an example light path between a light emitting planeand a light sensing plane in three-dimensional space. FIG. 24b depictsan example activation of discrete voxels intersected by the light pathin discretized three-dimensional space. FIG. 24c further depicts anexample activation of discrete voxels intersected by the light path indiscretized three-dimensional space. Additionally, FIG. 25a depictsdiscretized planes in a discretized space, shown with voxels activatedby multiple light paths. FIG. 25b depicts an example cross-sectionalview of a voxel arrangement in a discretized space. For each light pathsuch as those shown in FIG. 25a , the present invention will calculatewhich voxels the light path intersects, calculate the length of thelight path passing through each voxel, and calculate the opacity of eachvoxel that the light path intersects. In a planar arrangement, the lightemitting and light sensing arrays have n by n or n² LEDs and there willbe at most n⁴ light paths because each light path is defined by apairing of light emitting and light sensing LEDs and there are n²×n²=n⁴possible pairings of light emitting to light sensing LEDs. Consequently,there are also n⁴ number of equations. Further, the number of voxelswill vary from a minimum of n² wherein the distance between lightemitting and sensing arrays is at a minimum and a maximum of n⁴, whereinthe number of unknowns are equal to the number of equations.

It is important to keep in mind the fact that this model is a grossapproximation and oversimplification. It assumes that a light pathbetween a light-emitting and light-sensing LED is an infinitesimallysmall line when in reality each light path is actually a whole group oflight arrays with cylindrical thickness. This adds a second-ordercomplexity to the calculations which can be implemented in certainembodiments of the present application. But briefly, because each lightpath now has thickness, one must account for the fact that a light pathmay intersect several voxels in one place at a time. Therefore whencalculating the intersection length of the light path through eachvoxel, there are more parameters to consider.

1.5 Light Absorption Processes

Calculating the transmittance of a light path passing through severalvoxels can be calculated using Beer's law, which states that thetransmission factor (fraction of light transmitted) for a path of length1 and attenuation constant, a, is given by T=e^(−al). Each voxel has anassociated a value and a specific/value for every intersecting path oflight, whereas each path of light has an associated T value. That means,for any given light path, there is one associated T value but n numberof a and/values for n number of intersected voxels. In an exampleembodiment of the present invention, there are n³ voxels and at most n⁴light paths, which yields a system of equations with n³ unknown a valuesand at most n⁴ transmittance equations (derived from Beer's Law). If allthe T and 1 values are known for each equation within the system ofequations, the a values can be calculated for each voxel. Because thesystem of equations is overdetermined (there are more equations thanunknown variables), the a values should be calculated preferably using apseudo-inverse technique to minimize the error. The calculated a valuesdefine the opacity for each voxel. Once the opacity of each voxel forthe three dimensional space is calculated, the opacity of each voxel forthe object also becomes known, and this data allows for thereconstruction of a three dimensional visualization of the object.

Some aspects of Beer's Law can further be illustrated by FIGS. 26a and26b . FIG. 26a depicts an example cascade of identical lighttransmission loss layers illustrating Beer's law. As seen in Beer's law,the opacity of each voxel and the length of a light path travelingthrough that voxel affect the transmission loss of the light. Forexample, changing either the opacity factor or changing the length by afactor of 2 can decrease the fraction of light transmitted. FIG. 26bdepicts an example set of data based on FIG. 26a showing a relationshipbetween path length of light and light transmittance, wherein it isapparent that as the light path length increases, the transmittance oflight decreases.

Beer's Law can also be described by FIGS. 27a and 27b . In contrast toFIG. 26a , FIG. 27a depicts an example cascade of non-uniform light losstransmission through objects of different thicknesses. FIG. 27b depictsan example set of data based on FIG. 27a showing a relationship betweentransmittance and percentage of light loss, wherein it is apparent thatas the transmittance increases depending on the non-uniform thickness ofobjects, the percentage of correspondingly increases or decreases. SinceBeer's Law is not a linear relationship but rather a relationship ofexponential decay (T=e^(−al)), this means that depending on how manyvoxels are chosen to discretize a 3-D object or space, there will bedifferent calculated T values. The more finely discretized the space, orin other words, the smaller the voxels are, the more voxels each lightpath must intersect to get from the light-emitting array to thelight-sensing array. The more voxels it intersects, the more the lightgets attenuated, and the smaller the transmission value is.

2. First Model for Transmission-Based Tomography Computations

To better illustrate the above descriptions, this section explains anovel model of transmission-based tomography of 3-dimensional objectshaving at least partially transparent structures and surface boundaries(leveraging various associated conditions).

2.1 Indexing of Light Sensor Array and Light Emission Array

First assume a planar 2-dimensional light sensor array and a planar2-dimensional light-emission array facing each other in a parallelarrangement configured so each sensor in the light sensor plane canreceive light emitted by at least one light emitting element in thelight emitting plane. Each light sensor element in the light sensorarray has a unique index of the form {n_(s),m_(s)}, where n_(s)∈{1, 2, .. . , N_(s)} and m_(s)∈{1, 2, . . . , M_(s)}, and each light-emittingelement has a unique index of the form {n_(e), m_(e)}, where n_(e)∈{1,2, . . . , N_(e)} and m_(e)∈{1, 2, . . . , M_(e)}; accordingly the lightsensor array comprises a total of N_(s)M_(s) light-sensing elements andthe light emitting array comprises a total of N_(e)M_(e) light emittingelements.

2.2 Paths Between a Sensor in Light Sensor Array and Emitter in LightEmission Array Vs. Paths Between an Emitter in Light Emission Array anda Sensor in Light Sensor Array

Each ordered quadruple, denoted by

{{n _(e) ,m _(e) },{n _(s) ,m _(s)}}

comprising a specific emitting light and sensing light in theirrespective arrays, defines a light path within the 3-dimensionaldiscretized lattice. Think of the emitting light as the beginning of thelight path and the sensing light as the destination of the light path.This path will be denoted by

P({{n _(e) ,m _(e) },{n _(s) ,m _(s)}})

2.3 Intersection of Paths with Transparent Voxels

The 3-dimensional discretized lattice between the light emitting andlight sensing arrays consists of a 3-dimensional array of voxels. In anexample case, two n by n arrays of lights, one emitting and one sensing,facing each other at n distance apart will be discretized into n³adjacent individual cubes or voxels. These cubes are denoted by C_(ijk),where ijk denotes a specific index for each cube with the followingranges:

$\bigcup\limits_{\underset{\underset{k \in {\{{1,2,{\ldots N}}\}}}{j \in {\{{1,2,{\ldots N}}\}}}}{i \in {\{{1,2,{\ldots N}}\}}}}C_{ijk}$

The light path determined by {{n_(e),m_(e)}, {n_(s),m_(s)}} intersects asmall subset of the N³ cubes. A path that intersects cube C_(ijk)travels through cube C_(ijk) along a line segment inside the cube, andthe length of this line segment (which typically varies from cube tocube along the path) can be denoted as L_(ijk). As an example, FIG. 24cdepicts an example activation of discrete voxels intersected by thelight path in discretized three-dimensional space.

2.4 Total Transparency of a Path Intersecting Transparent Cubes

Again, a path that intersects cube C_(ijk) travels through cube C_(ijk)along a line segment inside the cube, and the length of this linesegment (which typically varies from cube to cube along the light path)can be denoted as L_(ijk).

There is a transmittance value for light, denoted as T_(ijk), that isassociated with each cube C_(ijk) and the length of the light pathL_(ijk) through the cube C_(ijk). Each cube has an associatedattenuation constant a_(ijk). In general this attenuation constant canvary with light wavelength, temperature, light polarization, and otherfactors. However for simplification dependency these factors will beomitted. As described above, according to Beer's law, the transmittancevalue T (fraction of light transmitted) for a path of length l andattenuation constant of value a is given by,

T=e ^(−al)

Thus for each cube C_(ijk) intersected by the path P({{n_(e),m_(e)},{n_(s),m_(s)}}) with a path segment of length L_(ijk), the transmittancevalue will be given by

T _(ijk)(L _(ijk))=e ^(−a) ^(ijk) ^(L) ^(ijk)

Thus the transmittance value of the total path can be calculated as theproduct of the transmittance values of each cube C_(ijk) in the path:

${T( {P( \{ {\{ {n_{e},m_{e}} \},\{ {n_{s},m_{s}} \}} \} )} )} = {{\prod{T_{ijk}( L_{ijk} )}} = {\prod\limits_{{\{{i,j,k}\}} \in {P{({\{{{\{{n_{e},m_{e}}\}},{\{{n_{s},m_{s}}\}}}\}})}}}^{{\{{i,j,k}\}} \in {P{({\{{{\{{n_{e},m_{e}}\}},{\{{n_{s},m_{s}}\}}}\}})}}}e^{{- a_{ijk}}L_{ijk}}}}$

2.5 Aperture Effects of Individual Light Sensors and Light Emitters

An important additional consideration is the aperture effects ofindividual light sensors and light emitters. If uniform manufacturingwith adequate tolerances can be assumed, additional mathematical modelscan be included (dependent, for example, on the angle of emitter orincident light paths). Alternately and advantageously, the system can becalibrated in a simpler approach. Amplitude measurements of the lightcan be made for each light path and stored with the sensing lights inthe sensing array when there is no object placed between the lightsensing and light emitting arrays. These measurements establish a “basecase” scenario that can then be used to provide calibratingnormalization factors for other non-base case scenarios. Thesepath-by-path normalization factors associated with these apertureeffects simply scale the measurement values used in the linearequations. For example, if a specific sensing light {n_(s), m_(s)}detects a light amplitude of A₀ for path P({{n_(e),m_(e)},{n_(s),m_(s)}}) without an object, and a light amplitude of A₁ with anobject, then the normalized amplitude A₁=A₀.

Ideally the light emitter emits light for a path P with unit amplitude;for such an ideal case:

(measured received light amplitude)=(emitted lightamplitude)·(transparency of path)

with

(emitted light amplitude)=1

and

(Transparency of Path)=T(P)

Giving T(P)=(Measured Received Light Amplitude)

However, the emitted light amplitude can be expected to vary from pathto path. Thus because of aperture effects it is more accurate toformulate the emitted light amplitude as a function of the path P, thatis A_(emit)(P). This gives

T(P)·A _(emit)(P)=(measured received light amplitude)

Similar path-dependent aperture effects can typically occur at thesensor as well. This can again be denoted with A_(sense)(P). Includingthis consideration gives

T(P)·A _(emit)(P)·A _(sense)(P)=(measured received light amplitude)

One can consolidate the two path-dependent aperture attenuations into asingle function

A(P), that is

A(P)=A _(emit)(P)·A _(sense)(P).

Such a function A(P) can be measured empirically for a given specificimplementation. Once known one can then write (for values of A(P)>0) therelation

${T(P)} = \frac{( {{measured}\mspace{14mu} {received}\mspace{14mu} {light}\mspace{14mu} {amplitude}} )}{A(P)}$

FIG. 28a depicts example aperture effects between a light emitting andlight sensing arrangement in an optical tomography system. FIG. 28bdepicts an example graph showing the relationship between magnitude oflight sensed by a light sensing arrangement and the incident angle ofthe light path. In reference to both FIGS. 28a and 28b , apertureeffects can be described by the phenomenon that as the incident angleincreases creating an angled path of light as opposed to a direct pathof light, the amount of light sensed decreases.

FIG. 29 depicts an example empirical aperture measurement andnormalization flow chart to account for aperture effects that may occurbetween light emitting and light sensing arrangement in discretizedthree-dimensional space. In other terms, FIG. 29 illustrates an exampleprocess of how the system is calibrated to account for aperture effects.An algorithm designed to normalize data takes in two inputs, atransmittance vector of a base case scenario when no object is presentbetween sensing and emitting arrays and, a transmittance vector of aspecific scenario when a specific object is being imaged. The algorithmuses the base case scenario to normalize the transmittance vector of thespecific scenario for more accurate measurements and calculations. Avariety of software programming languages and environments can be usedto implement the steps described in the flow chart and can be lateradapted for scattering effects.

2.6 Use of Logarithms to Transform Total Transparency of a Path into aLinear Equation

Taking the log of the above equation results in

${\log( \frac{{measurement}(P)}{A(P)} )} = {{{{\log ( {T(P)} )}\mspace{14mu} {giving}\mspace{14mu} {\log ( {{measurement}(P)} )}} - {\log ( {A(P)} )}} = {{\log ( {T(P)} )} = {{{\sum{{\log ( {T_{ijk}( L_{ijk} )} )}\{ {i,j,k} \}}} \in {P( \{ {\{ {n_{e},m_{e}} \} \{ {n_{s},m_{s}} \}} \} )}} = {{{\sum{{\log( e^{{- a_{ijk}}L_{ijk}} )}\{ {i,j,k} \}}} \in {P( \{ {\{ {n_{e},m_{e}} \} \{ {n_{s},m_{s}} \}} \} )}} = {{- {\sum{a_{ijk}L_{ijk}\{ {i,j,k} \}}}} \in {P( \{ {\{ {n_{e},m_{e}} \} \{ {n_{s},m_{s}} \}} \} )}}}}}}$

2.7 Use of Multiple Paths to Build a System of Linear Equations

Groups of equations such as constructed above

log(measurement(P)−log(A(P))=−Σa _(ijk) L _(ijk)

{i,j,k}ϵP({{n _(e) ,m _(e) }{n _(s) ,m _(s)}})

can be used to create a system of equations. That is, a selected groupof paths together form a collection P* of paths

P*={P _(({{n) _(e) _(,m) _(e) _(},{n) _(s) _(,m) _(s) _(}})}.)

For each path P∈P* (each P is P_(({{n) _(e) _(,m) _(e) _(},{n) _(s)_(,m) _(s) _(}}))), a transmittance value T(P) can be measured, and thecollection of lengths {L_(ijk)} for each cube intersected by the lightpath can be calculated with geometry.

2.8 Adequate Number of Equations

The individual attenuation constants {a_(ijk)} associated with eachcube, or voxel {C_(ijk)}, can then be treated as unknown variables,which can then be solved for if the collection of paths P* consist ofenough linearly-independent equations.

2.9 Over-Specified System of Equations

If the measurements can be expected to be noisy or non-ideal, it can beadvantageous for the collections of paths P* to have more equations thanunknown variables so as to create an over-specified system of(potentially inconsistent) linear equations. The over-specified systemcan be solved with a generalized inverse operation such as theMoore-Penrose Generalized Inverse, which finds the solution thatminimizes the error. In certain embodiments, however, it can beadvantageous to reduce computational processing and increase efficiency,which can be achieved through reducing the number of equations. FIG. 30adepicts an example planar geometry light emitting and light sensingarrangement wherein the emitting and sensing planes are of the samedimensions. FIG. 30b depicts an example planar geometry light emittingand light sensing arrangement wherein the emitting and sensing planesare of different dimensions. In having differing dimensions of theemitting and sensing planes, fewer equations are generated andtherefore, computations are reduced. Another way to reduce computationalprocessing is based on FIG. 31. FIG. 31 depicts an example planargeometry light emitting and light sensing arrangement wherein thedistance between emitting and sensing planes is reduced, therebyreducing the number of light paths and overall computational processing.

2.10 Example Sizings and Coordination of Indexing

The mathematics is simpler if n_(e)=n_(s) and m_(e)=m_(s) and if thelight sensor plane and light emitter planes are consistent and alignedso that the sensor element indices, emitter element indices, and cubeindices are subsets of a common indexed lattice. However, the inventionprovides for a wide range of variations, array sizes, configurations,and other choices for the light sensor arrays and a wide range ofdifferent variations, array sizes, configurations, and other choices forthe light emission arrays.

3. Example Physical Implementation

Now we will illustrate in greater detail the software and hardwareimplementation of the invention including an example of the data pathassociated with the invention.

3.1 Example Software Implementation

FIG. 32 depicts an exemplary measurement data scanning and acquisitionflow chart for data gathered by the light sensing array about an objectplaced between light emitting and light sensing arrangement indiscretized three-dimensional space. A first light-emitting LED isturned on in the emitting array. Then, a transmittance value iscollected for each light-sensing LED that senses light from the emittingLED. The transmittance value is then stored in a vector for computerprocessing. The first light-emitting LED then turns off and a differentlight-emitting LED turns on. This process repeats until alllight-emitting LEDs have been turned on at least once. In oneembodiment, a computer processing system can be used to providecoordinates to control the measurement data scanning and acquisition,including controlling of the LEDs turning on or off. FIG. 32 is exampleand is not limited by the order shown in the flow chart. A variety ofsoftware programming languages and environments can be used to implementthe steps described in the flow chart.

FIG. 33 depicts an example measurement data processing flow chart fordata gathered by the light sensing array about an object placed betweenlight emitting and light sensing arrangement in discretizedthree-dimensional space. In this example, a transmittance value for eachlight path is collected and stored into a vector T for processing. Thisvector T is fed to a processing algorithm (i.e., using Matlab™), whichcomputes attenuation values for each voxel and stores them in a vectora. Attenuation vector a is then fed to a 3D reconstruction algorithm(i.e., using Mathematica™), which creates a visualization of the 3Dobject. FIG. 33 is an example and is not limited by the order shown inthe flow chart. A variety of software programming languages andenvironments can be used to implement the steps described in the flowchart.

3.2 Example Hardware Implementation and Data Path

FIG. 34 depicts an example hardware and software architectureimplementation in an optical tomography system for a data path. Datapath generally refers to how data is processed from hardware to thesoftware associated with the invention. Referring to FIG. 34, thehardware would typically include but is not limited to the LED sensorarray, a field programmable gate array, an embedded processor, a USBstack, USB link, a computer—with a USB driver, USB, API, software forcontrolling the invention, memory, data storage, a display, etc. Theembedded CPU communicates with the FPGA and retrieves from the FPGA theinformation for each individual sensor. The embedded CPU uses its RAM toassemble all the individual sensor data into a frame. The concept of aframe provides the benefit of “synchronizing” the data elements into theconcept of one sensor image or frame, defined by a unique time stamp.That concept can then have additional attributes such as capturesettings, sequence number, etc. Technically it is also a natural conceptin the USB and Ethernet interfaces, with a natural 1-to-1 mapping. Eachframe is then sent by the embedded CPU to the computer via USB orEthernet. Typically, UDP packets would be a good choice to stream theframes efficiently over a reliable network. If reliability is an issue,TCP can be implemented and a “frame start pattern” can be added tosync/resync to the start of each frame within the byte-oriented TCPstream. The computer software application, can be written in aprogramming language such as C#/.NET, using a standard Microsoft™ USBdriver for the HID device class. Configuring the embedded CPU USB stackto present itself as a HID device has the advantage of being veryuniversally compatible with any operating system and its native drivers.The software application makes calls to the driver layer at regularintervals in order to retrieve any data that may have accumulated in theinternal queue of the driver. Then, the application performs sometransformations in order to generate the graphical data and display it.This includes linear mapping to color range, application of linearcalibration correction, etc.

FIG. 35 depicts an example method illustrating steps in the flow of thedata path of the invention.

Alternative embodiments using a variety of computing hardware andsoftware can be implemented depending on the amount of data, requiredperformance, etc.

4. Effects of Refraction, Reflection, and Light Scattering

The present application can also be configured to account in variousdegrees for various aspects of the effects of refraction, reflection,and light scattering.

FIG. 36a depicts an example of refraction of a light path transmittedthrough a transparent object between light emitting and light sensingarrangement.

FIG. 36b depicts an example of light scattering of a light pathtransmitted through a translucent object between light emitting andlight sensing arrangement.

FIG. 36c depicts an example of reflection of a light path through atransparent object between light emitting and light sensing arrangement.

5. Cylindrical Geometry Arrangements

5.1 Cylindrical Light Emitting and Sensing Arrangement

As mentioned previously, various embodiments of the invention caninclude a variety of geometric arrangements. One example of alternategeometric arrangements of value are those that are cylindrical. FIG. 37adepicts an example light emitting and light sensing arrangement withcylindrical geometry in an optical tomography system. FIG. 37b depictsthe arrangement of FIG. 37a with a row-like arrangement of LEDs in acylindrically shaped system. FIG. 37c depicts the LED arrangement ofFIG. 37b with an arrangement of LEDs on a front side and back side ofthe cylindrically shaped system. FIG. 37d depicts an example side viewof emitting LED from the back side of the cylindrically shaped system tothe front side. FIG. 37e depicts an example emitting LED emitting lightin and among LEDs in an emitting array from the back side of thecylindrically shaped system to the front side wherein a plurality ofsensing LEDs sense the emitted light among LEDs in a sensing array. FIG.37f depicts an example emitting LED emitting light from the back side ofthe cylindrically shaped system to the front side wherein a plurality ofsensing LEDs sense the emitted light.

A cylindrical arrangement can have a variety of embodiments. An exampleembodiment is FIG. 37g , which depicts a more detailed and rotated viewof the cylindrical arrangement of FIG. 37a , showing an emitting arrayand a sensing array. Each of the two arrays form curved planes based onthe curvature of the shape of the cylindrical structure implemented andshows an axis about which the cylinder is formed, for illustrationpurposes. FIG. 37g further shows a row-like arrangement of LEDs in moredetail than FIG. 37 b.

As with the planar light sensing and light emitting arrangementdescribed earlier, the cylindrical arrangement can also be discretizedinto cubes, or voxels, but without perfect alignment with the curvatureof the cylindrical structure. FIG. 37h depicts a top view of an examplediscretization of a light emitting and light sensing arrangement withcylindrical geometry in an optical tomography system. In FIG. 37h , itcan be seen that the voxels lying both inside and outside thecylindrical structure, do not have precise alignment with the curvatureof the cylindrical structure since the voxels lying both inside andoutside the cylindrical arrangement do not perfectly align with thecurvature of the cylindrical structure, the resulting attenuationconstants for these voxels lying inside and outside the cylindricalarrangement will be an approximation, and will provide less accuratevisualization of the object when the object is closer to the edge of thecylinder, as opposed to the object being placed towards the center ofthe cylindrical arrangement. Another approach that can be applied is toprorate the volume of the voxels that lie at the edge of the cylinder.This would provide an approximation with greater accuracy. Specifically,based on Beer's law, there is less accuracy because the l_(ilk) valuesfor the voxels lying inside and outside the cylindrical boundary of thecylindrical arrangement will be typically be an approximation since thelength of light path passing through these voxels is only passingthrough part of the voxel. The effect of such approximations can beaccounted for by various methods such as prorating the lengths lightpaths.

However, for many applications a cylindrical arrangement can beadvantageous as opposed to a planar arrangement, due to the curvature ofthe cylindrical arrangement, providing a more detailed view of theobject, since the LEDs are arranged at an angle, providing a greaternumber of direct light paths through the object. In other words, due tothe curvature of the cylindrical arrangement, the number of direct lightpaths traveling through the object is optimized and since a direct pathlight has the greatest brightness, this increases the accuracy of themeasurements taken by the system.

Further, in a cylindrical arrangement, LEDs can be co-optimized for bothemitting and sensing properties in order to provide a 360 scan of theobject, distinguishing it further from the planar arrangement describedabove.

While the planar arrangement view may be advantageous for planar objectssuch as a sample that has be sliced or flattened so as to beaccommodated on a microscope slide, a cylindrical arrangement mightprovide for better resolution for spherical objects such as a sampleexamined without slicing or flattening.

The mathematical computations involved with a cylindrical arrangementare very similar to those of a planar arrange and still use Beer's Law.Again, Beer's Law defines the relationship between the transmittance oflight with the length of a light path through an object and thatobject's opacity. Because of the different geometry, however, this lawmust be applied to different parameters. In the cylindrical case, wedefine three parameters: c, n, and A. The variable c represents thenumber of LEDs in a single row of LEDs in the cylindrical arrangement, nrepresents the number of rows of LEDs in the cylindrical arrangement,and A represents the number of voxels per row of LEDs (these as depictedin FIG. 37g ). Therefore, in a cylindrical case, the number of voxels isequal to A*n and the maximum number of equations is given by (n*(c/2))²because there are n*(c/2) light-emitting LEDs and n*(c/2) light sensingLEDs. n*(c/2)*n*(c/2) become the total possible number of pairingsbetween each light-emitting and light-sensing LED; each pair defines alight path.

To apply Beer's Law, similar to the planar case, one must calculate theintersection path length of light for each light path. To do this, onemust first define the position of each light-emitting LED andlight-sensing LED in space. In a planar geometry, this is simplerbecause the z coordinates for the light-emitting and light-sensingplanes are constant, so it is only necessary to calculate the x and ycoordinates. In a cylindrical geometry, the z coordinates are no longerconstant for each LED array because they are curved. Therefore, it isnecessary to calculate the x, y, and z coordinates dependently. Such acalculation often can be simpler when using polar coordinates and thenconvert polar to Cartesian coordinates. Once the coordinates for eachlight-emitting and light-sensing LED is defined, it becomes very simpleto calculate which voxels each light path intersects and the length oflight that intersects each voxel, and it is exactly the same as theplanar case.

To better illustrate discretization of a cylindrical arrangement, FIG.38 shows an example embodiment of a discretization of space in acylindrical light emitting and light sensing arrangement in an opticaltomography system. Further, FIGS. 39a-39c show multiple views of anexample embodiment of a discretization of space for a cylindrical lightemitting and light sensing arrangement in an optical tomography system.The amount of discretization can vary depending on the object beingimaged, accuracy of approximation desired, etc. FIGS. 40a-40b show anexample embodiment of a discretization of space for a cylindrical lightemitting and light sensing arrangement in an optical tomography system,wherein FIG. 40b shows increased discretization. As shown in the planararrangement above, FIGS. 41a-41b depict an example activation ofdiscrete voxels intersected by a light path in discretizedthree-dimensional space in a cylindrical arrangement in an opticaltomography system. Although the principle behind discretization remainsgenerally the same whether the arrangement is planar or cylindrical, thecomputations and approximations associated with a specific measurementusing a particular geometric arrangement can vary as illustrated above.

6. Example Holding Arrangements and Modules

The present invention can comprise a holding module for a variety ofimplementations and applications.

FIG. 42a illustrates an example sample holding module, as a slide with awell for a planar light emitting and light sensing arrangement in anoptical tomography system for cytometry. In one embodiment, the holdingmodule in FIG. 42a , is a well embedded into a transparent removablemodule with leg-type acting as supports for the removable module, whichextend outside the boundaries of the LED arrays. In other embodiments,the holding module in FIG. 42a , as well the support structure can havedifferent dimensions.

FIG. 42b illustrates a side view of the example holding module of FIG.42 a.

FIG. 43a illustrates an example holding module, as a pathway for aplanar light emitting and light sensing arrangement in an opticaltomography system. FIG. 43b illustrates a side view of the exampleholding module of FIG. 43a . The portions of pathway that extend pastthe 2 arrays can be parallel with the arrays, or can also be angled, asshown in FIG. 43b , to prevent compromise of samples (spilling, etc.)from gravity or other factors. The configuration in FIG. 43a can beuseful in flow cytometry and microfluidic applications.

FIG. 44a illustrates an example holding module, as a belt configurationfor a planar light emitting and light sensing arrangement in an opticaltomography system. In FIG. 44a , a belt configuration, as seen front thefront or back, with two conveyer belts, a transparent removable modulethat travels through the light-emitting and light-sensing arrays by wayof 2 or more conveyor belts, which can extend outside the boundaries ofthe LED arrays to prevent corrupting a scan of the object. The samplecan be deposited onto the module by way of a well, a pathway, or simplyplaced onto the module, in a way similar to a microscope slide.

FIG. 45a illustrates an example holding module, as a shell configurationfor a planar light emitting and light sensing arrangement in an opticaltomography system. The shell configuration illustrated in FIG. 45a atransparent removable module in the form of a transparent enclosure,which can have a variety of shapes depending on the harnessing of themodule to the light emitting and sensing arrangement. One embodiment ofthis configuration is a cube with a removable lid, into which a samplecan be inserted.

FIG. 45b illustrates another example holding module comprising a shellconfiguration for a planar light emitting and light sensing arrangementin an optical tomography system. The shell configuration illustrated inFIG. 45b comprises a transparent removable module in the form of atransparent enclosure, which can then be inserted between the arrays forscanning, in a stackable arrangement, as demonstrated by this figurewhich can have a variety of shapes depending on the harnessing of themodule to the light emitting and sensing arrangement.

FIG. 45c illustrates yet another example holding module comprising ashell configuration for a planar light emitting and light sensingarrangement in an optical tomography system. In the configuration inFIG. 45c , the removable module holding a sample can be of a variety ofsizes, and can be inserted into the configuration.

FIG. 46a illustrates an example holding module comprising a handleconfiguration for a planar light emitting and light sensing arrangementin an optical tomography system. In the configuration of FIG. 46a , theremovable module holding a sample can be of any size, and can beinserted into the configuration. Such an arrangement can be applied to avariety of configurations, to increase ease-of-use outside thetraditional environment of a lab.

FIG. 46b illustrates an example holding module comprising a hookconfiguration for a planar light emitting and light sensing arrangementin an optical tomography system.

FIG. 46c illustrates the example holding module of FIG. 46a , whereinthe handle is placed at a different location. Many other types of handlearrangements are anticipated and provided for by the invention,including wand, paddle, and various “dustpan”-like configurations.

FIG. 46d illustrates an example holding module, a comprising a“bell-jar”-like configuration. FIG. 46e illustrates the light emittingand sensing arrays of the holding module of FIG. 46d . In the case ofthe bell-shaped configuration, the light-emitting LEDs and light-sensingarrays can be arranged in such a way that one half of the bellcomprising of light-emitting LEDs, and the other half comprising oflight-sensing LEDs, as shown in this figure. In the form of a bellconfiguration, the arrangement can be placed over a sample.

The configurations of the holding modules can be adapted and combined invarious ways depending on the application and size of the objects to beinserted. The holding modules can be made of various materials in orderto optimize performance and maintain or improve the accuracy ofmeasurements by the system.

7. Light-Path Visualizers

The present invention can further comprise a visualizer module toprovide image viewing, editing, and processing capabilities for handling3D data, voxel operations, local filtering, morphology, etc. Thevisualizer module can comprise various controls via a graphical userinterface of the module, associated with varying the view and dimensionsof the visual rendering. The visualization module can also includecontrols and sliders associated with mathematical properties of thevisual rendering. FIGS. 47a, 47b, 48a, 48b, 48c, 49a, and 49b depictvarious example graphical renderings in a visualizer module. Forexample, as can be seen in FIGS. 47a, 47b, 48a, 48b, 48c, 49a, and 49b ,coordinates associated with discretized space can be controlled viasliders on the top portion of a viewing window. Of course, thevisualizer controls shown here are only examples and can be modifieddepending on the functionality desired.

8. Example Applications

The present invention can be utilized in a variety of applications, suchas in microscopy, microplates, fluorescence detection, microfluidics,cytometry, and flow cytometry. Other applications are anticipated andprovided for by the invention.

8.1 Microscopy

Microscopy typically involves the use of optical microscopes and otherrelated imaging systems in the study of small organisms, samples, andother objects that cannot be seen without magnification by the unaidedeye. Microscopy has several branches, including for example opticalmicroscopy and electron microscopy, each of which in turn have varioussub-branches.

The present invention can be readily applied to the branch of opticalmicroscopy, which images samples using properties of light. In thetraditional sense, optical microscopes use a single or multiple lensesto magnify a sample so that it becomes visible to the naked eye.

Various embodiments of the present invention, as described, can be suchthat they do not use lenses. The invention, as applied to microscopy canimage transparent samples. The resolution, determined by the size of theLEDs being used within the sensing and emitting arrays, also haspotential to be high with the use of printed OLEDs (organiclight-emitting diodes). Printed OLEDs are currently used to achieve thehigh-resolution of television and smartphone screens, so it is entirelyfeasible to print OLEDs at the same fine resolution to recreate ahigh-resolution three-dimensional model of a microscopic object.

The invention's ability to three-dimensionally model an object will havevery important applications in life sciences. Cells and cellularcomponents, which are naturally transparent, can easily be imaged andmodeled with the invention at very high-resolution. Currently there aresimilar microscopy technologies that also achieve three-dimensionalmodeling, including confocal microscopy, which also uses a scanningpoint of light. However, the cost of these technologies can beprohibitively high. The present invention has the potential to achievethe same resolution and same detailed three dimensional modeling at amuch lower cost.

The ability to image a full three-dimensional model of a cell ororganism can be invaluable when paired with fluorescence microscopytechniques. In fluorescent microscopy, fluorescent chemical compoundswhen combined with for example, antibodies, can be utilized asbiological probes or to stain specific targets (i.e., cells, organelles,organisms, etc.) to be imaged for identifying the regions and structureswithin a cell or organism that have specific properties or chemicalcompositions.

It is understood that one skilled in the art can apply a differentgeometric configurations and/or other different arrangements to formalternate embodiments.

8.2 Fluorescence Detection Example

One could also use fluorescence techniques to mark specific regions witha cell or organism and then use the invention to image, model, andlocate the fluorescing regions. If ultraviolet (UV) excitation isutilized, to block unwanted effects of UV stimulation, a UV filter canalso be applied to the invention. FIG. 50 depicts an example embodimentof a fluorescence detection application with a planar light emitting andlight sensing arrangement in an optical tomography system. As shown inFIG. 50, varying types of target-specific fluorescent dyes can beapplied to samples in the wells of a microplate. Specific organelles arerecognized after their emitted fluorescent light is sensed. In thisembodiment, a planar tomography configuration is depicted. Cylindricaland other arrangements for each well can also be applied.

It is understood that one skilled in the art can apply a differentgeometric configurations and/or other different arrangements to formalternate embodiments.

8.3 Cytometry and Flow Cytometry Example

Cytometry typically refers to the methods that are used to measurevarious characteristics of a cell, including cell size, current stage ofthe cell cycle, DNA content, and protein content. This is another veryfitting application for the present invention. Cells are typicallynaturally transparent, making it very easy to derive a high-resolutionthree-dimensional model of the cell's interior contents and exteriormembrane using our imaging techniques. This model can be used toaccurately measure the three-dimensional shape of the cell, and caneasily be examined to determine the stage of the cell cycle. Again,fluorescent markers can be coupled with the invention to identifyproteins and other chemicals within the cell. Similar to microscopy, thepresent invention can achieve ranges of microscopic resolution usingprintable OLEDs.

In one embodiment, the present application can also be applied to flowcytometry. Flow cytometry is the method of imaging cells as they move(or flow) in a liquid through the microscope. It is generally used forquickly amassing large amounts of data about a large number of cells.The invention could be adapted to allow for rapid imaging of movingobjects to obtain high-resolution video-streams of cells.

FIG. 51 depicts an example embodiment of a flow cytometry applicationwith a cylindrical light emitting and light sensing arrangement in anoptical tomography system. Antibodies with fluorescent markers attach tospecific target cells. Specific targets are recognized after lightemitted from the fluorescent marker is sensed. Planar and otherarrangements can also be applied.

It is understood that one skilled in the art can apply a differentgeometric configurations and/or other different arrangements to formalternate embodiments.

8.4 Microplate Example

Microplates also provide a suitable application for the presentapplication. In one embodiment, cylindrical geometry can be utilized inan embodiment of the present invention with microplates. FIG. 52aillustrates an example embodiment of the present invention as amicroplate. FIG. 52b illustrates a side view of FIG. 52a . A cylindricalgeometric arrangement of the present invention can be useful asimplemented in individual wells of a microplate arrangement commonlyused in chemical and life science settings. Such an application canprovide a more powerful and detailed approach to imaging the samplewithin a well. In one embodiment, the light emitting and sensing arraysof the present application can be arranged with planar geometry asdepicted in FIG. 52. FIG. 53 depicts an example embodiment of amicroplate with a planar light emitting and light sensing arrangement inan optical tomography system. FIG. 54 depicts another example embodimentmicroplate with a planar light emitting and light sensing arrangement inan optical tomography system.

In another embodiment, a microplate with a planar light emitting andlight sensing arrangement can be applied to each well of the microplatein an optical tomography system as depicted in FIG. 55 a.

In other embodiments, printing LEDs to form emitting and sensing arraysonto flexible and printable material could leverage the cylindricalgeometry in the shape and scale of microplates. For example, FIG. 55bdepicts an example embodiment of a microplate with a cylindrical lightemitting and light sensing arrangement applied to each well of themicroplate in an optical tomography system. Having a cylindricalarrangement can increase the angles from which the sample is scanned, asillustrated above generally for cylindrical arrangements.

It is understood that one skilled in the art can apply a differentgeometric configurations and/or other different arrangements to formalternate embodiments.

8.5 Culture Dish and Petri Dish Example

Either cylindrical or planar arrangements of the present application canalso be applied to culture or Petri dishes commonly used in labsettings. For example, FIG. 56a depicts an example embodiment of aculture dish with a planar light emitting and light sensing arrangementin an optical tomography system. In yet another embodiment, FIG. 56bdepicts an example embodiment of a culture dish with a cylindrical lightemitting and light sensing arrangement in an optical tomography system.

It is understood that one skilled in the art can apply a differentgeometric configurations and/or other different arrangements to formalternate embodiments.

8.6 Microfluidic Example

The present application also can be applied to microfluidicapplications. As an example, FIG. 57 depicts an example microfluidicplate with a planar light emitting and light sensing arrangement in anoptical tomography system. In FIG. 57, a planar geometry arrangement isapplied to a reaction chamber on a microfluidic plate, used to detectreaction of substances in the reaction chamber.

It is understood that one skilled in the art can apply a differentgeometric configurations and/or other different arrangements to formalternate embodiments.

8.7 Incubation Chamber Example

FIG. 58 depicts another example microfluidic plate with a planar lightemitting and light sensing arrangement in an optical tomography system.FIG. 58 shows how the optical tomography system of the presentapplication is used to scan the change in culture in a microfluidicincubation chamber. Although a planar configuration is applied to themicrofluidic plate, other geometric arrangements can also beimplemented.

In yet another embodiment, the present application can also be appliedto a microfluidic structure or assembly found on lab-on-a-chip devices.

It is understood that one skilled in the art can apply a differentgeometric configurations and/or other different arrangements to formalternate embodiments.

8.8 Culture Chamber Example

Another biological application of the present application system isshown in FIG. 59, which depicts an example embodiment of a culturechamber, with a planar light emitting and light sensing arrangement inan optical tomography system. FIG. 59 shows the culture chamberenveloped in biological membranes that are selectively-permeable tomedia that flows through a channel surrounding them, wherein the presentapplications scans the culture chamber. This configuration can embodyvalves to control media flow.

It is understood that one skilled in the art can apply a differentgeometric configurations and/or other different arrangements to formalternate embodiments.

CLOSING

The terms “certain embodiments”, “an embodiment”, “embodiment”,“embodiments”, “the embodiment”, “the embodiments”, “one or moreembodiments”, “some embodiments”, and “one embodiment” mean one or more(but not all) embodiments unless expressly specified otherwise. Theterms “including”, “comprising”, “having” and variations thereof mean“including but not limited to”, unless expressly specified otherwise.The enumerated listing of items does not imply that any or all of theitems are mutually exclusive, unless expressly specified otherwise. Theterms “a”, “an” and “the” mean “one or more”, unless expressly specifiedotherwise.

The foregoing description, for purpose of explanation, has beendescribed with reference to specific embodiments. However, theillustrative discussions above are not intended to be exhaustive or tolimit the invention to the precise forms disclosed. Many modificationsand variations are possible in view of the above teachings. Theembodiments were chosen and described in order to best explain theprinciples of the invention and its practical applications, to therebyenable others skilled in the art to best utilize the invention andvarious embodiments with various modifications as are suited to theparticular use contemplated.

While the invention has been described in detail with reference todisclosed embodiments, various modifications within the scope of theinvention will be apparent to those of ordinary skill in thistechnological field. It is to be appreciated that features describedwith respect to one embodiment typically can be applied to otherembodiments.

The invention can be embodied in other specific forms without departingfrom the spirit or essential characteristics thereof. The presentembodiments are therefore to be considered in all respects asillustrative and not restrictive, the scope of the invention beingindicated by the appended claims rather than by the foregoingdescription, and all changes which come within the meaning and range ofequivalency of the claims are therefore intended to be embraced therein.

In addition, it will be appreciated that the various operations,processes, and methods disclosed herein may be embodied in amachine-readable medium and/or a machine accessible medium compatiblewith a data processing system (e.g., a computer system), and may beperformed in any order (e.g., including using means for achieving thevarious operations). Accordingly, the specification and drawings are tobe regarded in an illustrative rather than a restrictive sense.

Although example embodiments have been provided in detail, variouschanges, substitutions and alternations could be made thereto withoutdeparting from spirit and scope of the disclosed subject matter asdefined by the appended claims. Variations described for the embodimentsmay be realized in any combination desirable for each particularapplication. Thus particular limitations and embodiment enhancementsdescribed herein, which may have particular advantages to a particularapplication, need not be used for all applications. Also, not alllimitations need be implemented in methods, systems, and apparatusesincluding one or more concepts described with relation to the providedembodiments. Therefore, the invention properly is to be construed withreference to the claims.

1. An optical tomography system, comprising: an illuminating lightemitting array including a plurality of light emitting elements arrangedto transmit a controllable emitted light field into a well of amicroplate onto contents within the microplate well; and a light sensingarray for measuring a received light field from the opposite side of themicroplate well, the received light field created from light emergingfrom the contents of the microplate well responsive to controllableemitted light field, wherein the light sensing array is configured tosense light emitted from the illuminating light emitting array after thelight has passed through the contents of the microplate well.
 2. Theoptical tomography system of claim 1, wherein the plurality of lightemitting elements in the illuminating light emitting array aresequentially illuminated.
 3. The optical tomography system of claim 1,wherein the illuminating light emitting array is configured, viasequencing, to operate both as an illuminating light source and as areflective-imaging light sensor.
 4. The optical tomography system ofclaim 1, wherein the illuminating light emitting array is configured,via multiplexing, to operate both as an illuminating light source and asa reflective-imaging light sensor.
 5. The optical tomography system ofclaim 1, wherein at least one light emitting element of the plurality oflight emitting elements in the illuminating light emitting array is alight emitting diode (LED).
 6. The optical tomography system of claim 1,wherein at least one light emitting element of the plurality of lightemitting elements in the illuminating light emitting array is an organiclight emitting diode (OLED).
 7. The optical tomography system of claim1, wherein at least one light emitting element of the plurality of lightemitting elements in the illuminating light emitting array is an organiclight emitting transistor (OLET).
 8. The optical tomography system ofclaim 1, wherein the light sensing array comprises a light sensorcomprising organic semiconductor material.
 9. The optical tomographysystem of claim 1, wherein the light sensing array comprises aphotodiode.
 10. The optical tomography system of claim 1, wherein thelight sensing array comprises a phototransistor.
 11. The opticaltomography system of claim 1, wherein the light sensing array comprisesa complementary metal-oxide-semiconductor (CMOS) photodetector.
 12. Theoptical tomography system of claim 1, wherein the light sensing arraycomprises a charge-coupled device.
 13. The optical tomography system ofclaim 1, wherein the illuminating light emitting array is planar array.14. The optical tomography system of claim 1, wherein the light sensingarray is a planar array.
 15. The optical tomography system of claim 1,wherein the illuminating light emitting array is a non-planar array. 16.The optical tomography system of claim 1, wherein the light sensingarray is a non-planar array.
 17. The optical tomography system of claim1, wherein the system is configured to provide an over-specified systemof equations relating light-adsorption voxel values to light measurementvalues.
 18. The optical tomography system of claim 16, wherein theover-specified system of equations is linearized via use of mathematicaloperations to produce a linearized over-specified system of equations.19. The optical tomography system of claim 17, wherein the linearizedover-specified system of equations is solved for approximatelight-adsorption voxel values using at least a generalized inverseoperation.
 20. The optical tomography system of claim 1, wherein themicroplate well is cylindrical.